Question 466658: 8. For the following function find the vertical, horizontal, and oblique asymptotes, if any. Please show all of your work.
f(x)=16x²/3x²-17x+10 (+7)
I appreciate any help!Thanks
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! For the following function find the vertical, horizontal, and oblique asymptotes, if any. Please show all of your work.
f(x)=16x²/3x²-17x+10 (+7)
f(x)=16x^2/(3x^2-17x+70)
When the degree of numerator and denominator are equal, as in this case, the horizontal asymptote is found by dividing the leading coefficient of the numerator by the leading coefficient of the denominator.
Horizontal asymptote=16/3=5.333..
Vertical asymptotes are found by setting the denominator=0, then solve for x. In this case, there are no real roots in the denominator, so there are no vertical asymptotes. You can also see that the denominator could not go to zero because of its constant,70.
See the graph below as a visual check on the answers
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y=16x^2/(3x^2-17x+70)
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